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Lecture 3 Supplement. Prof. Hsien-Hsin Sean Lee School of Electrical and Computer Engineering Georgia Institute of Technology. Rotation Along an Arbitrary Axis. Transform the axis to cross origin (0,0,0) Transform the axis around X onto the XZ plane
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Lecture 3 Supplement Prof. Hsien-Hsin Sean Lee School of Electrical and Computer Engineering Georgia Institute of Technology
Rotation Along an Arbitrary Axis • Transform the axis to cross origin (0,0,0) • Transform the axis around X onto the XZ plane • Transform the axis around Y onto the Z axis • Perform Rotation (angle=) • Inverse Transform of 3. • Inverse Transform of 2. • Inverse Transform of 1.
y x z Step 1: Translate to (0, 0, 0) • For easier viewing, I use RHS. Rotating axis
y x z Step 2: Rotate around X, project to XZ y (a, b, c) b z x (into the screen) c • Let’s pick up a random point (a, b, c) on the axis to figure out cos
Step 3: Transform around Y onto the Z axis y a x y (into the screen) x (a’, 0, c’) z z